Methods and apparatuses of ALF derivation in video encoding system

3. The method of claim 2, wherein the steps for each subsequent iteration of the ALF clipping index optimization are repeated until clipping indices of the initial setting are determined to be the final clipping indices.

4. The method of claim 1, wherein deriving said plurality of clipping setting candidates from the initial clipping setting comprises deriving each clipping setting candidate by only adjusting one clipping index of the initial clipping setting.

5. The method of claim 1, wherein the inverse matrices associated with the clipping settings sharing the partial intermediate results are collectively solved in parallel.

6. The method of claim 1, wherein the inverse matrices associated with the clipping settings sharing the partial intermediate results are collectively solved sequentially.

7. The method of claim 1, wherein each of the clipping settings contains twelve clipping indices when the reconstructed video samples are luminance (luma) samples, each of the clipping settings contains six clipping indices when the reconstructed video samples are chrominance (chroma) samples, or each of the clipping settings contains seven clipping indices when applying Cross Component ALF (CCALF) to the reconstructed video samples.

8. The method of claim 1, wherein the partial intermediate results of solving ALF coefficients shared by the two or more clipping settings correspond to matrix entries with same entry operations to be performed in a row elimination step of Gaussian elimination.

13. The method of claim 12, wherein the steps for the subsequent iteration of the ALF coefficient quantization optimization process are repeated until the final quantized values for the ALF coefficients are determined to be quantized values of the initial setting.

14. The method of claim 9, wherein deriving a plurality of setting candidates from the initial setting comprises deriving each setting candidate by only adjusting one quantized value of the initial setting.